text: # Copyright 2018 The TensorFlow Probability Authors.
  #
  # Licensed under the Apache License, Version 2.0 (the "License");
  # you may not use this file except in compliance with the License.
  # You may obtain a copy of the License at
  #
  #     http://www.apache.org/licenses/LICENSE-2.0
  #
  # Unless required by applicable law or agreed to in writing, software
  # distributed under the License is distributed on an "AS IS" BASIS,
  # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
  # See the License for the specific language governing permissions and
  # limitations under the License.
  # ============================================================================
  """Tanh bijector."""
  
  from __future__ import absolute_import
  from __future__ import division
  from __future__ import print_function
  
  import numpy as np
  import tensorflow.compat.v2 as tf
  from tensorflow_probability.python.bijectors import bijector
  from tensorflow_probability.python.internal import auto_composite_tensor
  
  
  __all__ = [
      'Tanh',
  ]
  
  
  @auto_composite_tensor.auto_composite_tensor(
      omit_kwargs=('name',), module_name='tfp.bijectors')
  class Tanh(bijector.AutoCompositeTensorBijector):
    """Bijector that computes `Y = tanh(X)`, therefore `Y in (-1, 1)`.
  
    This can be achieved by an affine transform of the Sigmoid bijector, i.e.,
    it is equivalent to
    ```
    tfb.Chain([tfb.Shift(shift=-1.),
               tfb.Scale(scale=2.),
               tfb.Sigmoid(),
               tfb.Scale(scale=2.)])
    ```
  
    However, using the `Tanh` bijector directly is slightly faster and more
    numerically stable.
    """
  
    def __init__(self, validate_args=False, name='tanh'):
      parameters = dict(locals())
      with tf.name_scope(name) as name:
        super(Tanh, self).__init__(
            forward_min_event_ndims=0,
            validate_args=validate_args,
            parameters=parameters,
            name=name)
  
    @classmethod
    def _is_increasing(cls):
      return True
  
    @classmethod
    def _parameter_properties(cls, dtype):
      return dict()
  
    def _forward(self, x):
      return tf.math.tanh(x)
  
    def _inverse(self, y):
      return tf.atanh(y)
  
    # We implicitly rely on _forward_log_det_jacobian rather than explicitly
    # implement _inverse_log_det_jacobian since directly using
    # `-tf.math.log1p(-tf.square(y))` has lower numerical precision.
  
    def _forward_log_det_jacobian(self, x):
      #  This formula is mathematically equivalent to
      #  `tf.log1p(-tf.square(tf.tanh(x)))`, however this code is more numerically
      #  stable.
      #  Derivation:
      #    log(1 - tanh(x)^2)
      #    = log(sech(x)^2)
      #    = 2 * log(sech(x))
      #    = 2 * log(2e^-x / (e^-2x + 1))
      #    = 2 * (log(2) - x - log(e^-2x + 1))
      #    = 2 * (log(2) - x - softplus(-2x))
      return 2. * (np.log(2.) - x - tf.math.softplus(-2. * x))
  